What's the difference between 3, 1/3, the sum from n=1 to infinity of 1/n^3, and pi? We will start with a discussion of what it means for a number to be integral, rational, algebraic, or transcendental. We will talk about the history of the multiple zeta values (certain real numbers) and some open problems about them. You will leave this talk knowing more about the real numbers than you thought was possible, but also with more questions about the real numbers than you thought was possible!
We will introduce the area of arithmetic statistics and the Cohen- Lenstra heuristics. We will give some background about the work of Bhargava- Shankar-Tsimerman and Taniguchi-Thorne on the Davenport-Heilbronn theorems. We will then explain our recent proof that 96.2% of totally real cubic fields have genus number one and, if time permits, talk about some applications. This represents joint work with Kevin McGown.
Multiple zeta values